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Tuymaada Olympiad
2002 Tuymaada Olympiad
2
Four variables plus a restraint
Four variables plus a restraint
Source: Tuymaada 2002
April 26, 2006
inequalities
inequalities unsolved
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be positive real numbers such that
a
b
c
d
=
1
abcd=1
ab
c
d
=
1
. Prove that
1
+
a
b
1
+
a
+
1
+
b
c
1
+
b
+
1
+
c
d
1
+
c
+
1
+
d
a
1
+
d
≥
4.
\frac{1+ab}{1+a} + \frac{1+bc}{1+b} + \frac{1+cd}{1+c} + \frac{1+da}{1+d} \geq 4 .
1
+
a
1
+
ab
+
1
+
b
1
+
b
c
+
1
+
c
1
+
c
d
+
1
+
d
1
+
d
a
≥
4.
Proposed by A. Khrabrov
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